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How does the force of gravitation between two objects change when the distance between then is reduced to half ?
We know that,
Gravitational force F = G (m1m2/r2) …(i)
According to question,
if the distance between them is reduced to half, then,
r1 = r/2
∴ F1 = G (m1m2/(r/2)2)
F1 = (Gm1m2/r2).4 …(ii)
From equation (i) and (ii)
F/F1 = 1/4
⇒ F1 = 4F
Thus the force of attraction between them increases to four times.
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